Cremona's table of elliptic curves

10416 = 2⁴ · 3 · 7 · 31

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 31+	Signs for the Atkin-Lehner involutions
Class	10416p	Isogeny class
Conductor	10416	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	31488032636928 = 224 · 32 · 7 · 313	Discriminant
Eigenvalues	2- 3+  0 7+ -6  2  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-68488,6916336]	[a1,a2,a3,a4,a6]
j	8673882953919625/7687507968	j-invariant
L	1.3091620217042	L(r)(E,1)/r!
Ω	0.6545810108521	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1302h3 41664dg3 31248bi3 72912cw3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10416p3

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	+	0	+	-6	2	6	4	6	0	+	2	0	4	-6	12	-6	-10	4	-12	2	-8	0	-18	-10

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Quadratic twists for elliptic curve 10416p3

-4	8	-3	-7
1302h3	41664dg3	31248bi3	72912cw3

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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